Ordinary Condoms (otherwise known as Armour, Baudruches, Redingotes Anglaises):
First, take a sheep’s small intestine. Soak it in water for several hours. Turn it inside out, and then mash it gently in weak alkaline. Change the alkaline solution every 12 hours (For personal use of just a few condoms, don't bother changing the weak alkaline solution. Mashing needn't take that long. Unless you're a really horny bugger and need a lot of them, or are planning on going into the business of producing sheep gut condoms.). Scrape it carefully to removed the mucous membrane, leaving the peritoneal and muscular coats. Expose it to the vapour of burning brimstone, then wash it with soap and water. Blow it up, dry it, cut to a length of 7-8 inches, and finally border it at the open end with a ribbon (or riband, as the Victorians would have said).

Baudruches fines:
Soak the intestine in a weak lye solution. Turn it inside out, and then prepare it as before. Soak in lye again, apply brimstone, draw out smooth upon oiled moulds of a proper size, with the external coat of the gut next to the mould.

Baudruches superfines:
Soak it for 24 hours, changing the water twice. Carefully dress it with a sharp knife. Soak in hard water for 3 days, changing the water often. Dry it with a clean cloth, scent it with essences, and stretch it on a glass mould. Finally, rub it with a glass to polish it.

Baudruches superfine doubles:
When the intestine is in its moist state on the mould, another similarly prepared moist condom should be drawn over the first. The two insides will adhere together.

These do not stop the transmission of viruses! So, they do not prevent the transmission of HIV and AIDS. (They have little pores that are bigger than the little viruses.) They might stop other, bacteria-borne STDs, but I wouldn't count on it.

The condom is an ancient device and traces back to ancient Rome (with goat bladder), Egypt (linen) and Japan (oiled silk paper). Sheaths of sheep-gut where used in England (and likely most of Europe) during the 17th century where their use as prophylactics and as a guard against sexually transmitted diseases where documented by many of the time. Madame de Sevigne, a writer of the time, describes them as "an armour against enjoyment and a spider-web against danger". Chances
are she was a bit dissatisfied with their performance and took note of the effectiveness against STDs.

exposed to a sulphuric vapor (kill anything that survived the
alkaline solution?)

wash

stretched

dry

cut to length

tie one end

Upon use of the condom, it was necessary to soak them to return them back to their stretchy nature. All of this labor resulted in a very expensive product at the time, however it was reusable. Some companies at the time built quite a market for re-used condoms.

With the use of rubber in the late 19th and early 20th century, condoms have moved away from the gut to cheaper and more reliable rubber and then latex condoms.

Organic condoms can still be found and are used by individuals with latex allergy (a potentially life threatening situation where a person can be killed by coming in contact with latex). These are often marketed as "natural membrane" condoms or as "lambskin". While these condoms provide an adequate barrier against cell sized things (such as sperm) they provide no protection against smaller things such as viruses and bacteria. The natural holes between the cells are large enough for viruses and bacteria and viruses are designed for getting in, through and around cells. These condoms are not recommended if there is any risk of a venereal disease - especially those caused by viruses such as AIDS. In these cases, the polyurethane (non-latex) condom is recommended.

From one such maker:

Fourex Natural Skin condoms are recommended only for the prevention of pregnancy. Clinical evidence to support its use for the prevention of every sexually transmitted disease is not currently available.